The Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question: What methods are there for comparing things?
Notes:
If you have questions about a problem, or don’t understand it, you SHOULD ask questions.
Mathematical Reflections 1
In this investigation, you explored several ways of comparing numbers.
Here are five methods for making comparisons, with examples:
Ratios: In taste tests, people who preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 3 to 2.
Differences: Students who prefer television outnumber those who prefer radio by 20.
Fractions: 3/5 of cola drinkers prefer Bolda Cola to Cola Nola.
Percents: 28% of people aged 12-17 go camping.
Scaling: The number of students who prefer watching television is 1.5 times the number who prefer listening to the radio.
Give another example of each type of comparison listed above.:
Ratios: Students prefer radio to television by a ratio of 2 to 3.
Differences: People who prefer Bolda Cola outnumber those who prefer Cola Nola by 5,713.
Fractions: About 1/5 of the people aged 18-24 go camping at least twice a year.
Percents: 60% of all cola drinkers prefer Bolda Cola to Cola Nola.
Scaling: The number of people aged 12-17 that go camping at least twice a year is 1.64 times as many as the number of people aged 18-24 that go camping twice a year.
2. What information do you get from a ratio comparison that you don’t get from a difference comparison?:
In a ratio, you know both numbers in the comparison, and gives you a better proportion and how much one number is out of. In a difference, you only know the amount between the numbers, and you don't know anything about proportion. But if there are more than two numbers in the comparison, things change a bit and get more complicated.
Think about your answers to these questions, discuss your ideas with other students and your teacher, and write a summary of your findings in your journal.:
Ratios, differences, fractions, percents, and scaling are 5 different methods of comparison. They are all more or less accurate and useful comparison methods. It’s good that you can represent comparisons in more than one way, because some comparisons cover more than others. When comparing different things, you’ll need to use all the methods of comparisons because one comparison can give different information than the other. So, a bit like a table, graph, and a written report, all comparison methods are useful at different times.
S.B.K.
The Big Idea:
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question:
What methods are there for comparing things?
Notes:
If you have questions about a problem, or don’t understand it, you SHOULD ask questions.
Mathematical Reflections 1
In this investigation, you explored several ways of comparing numbers.
Here are five methods for making comparisons, with examples:
Ratios: In taste tests, people who preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 3 to 2.
Differences: Students who prefer television outnumber those who prefer radio by 20.
Fractions: 3/5 of cola drinkers prefer Bolda Cola to Cola Nola.
Percents: 28% of people aged 12-17 go camping.
Scaling: The number of students who prefer watching television is 1.5 times the number who prefer listening to the radio.
Ratios: Students prefer radio to television by a ratio of 2 to 3.
Differences: People who prefer Bolda Cola outnumber those who prefer Cola Nola by 5,713.
Fractions: About 1/5 of the people aged 18-24 go camping at least twice a year.
Percents: 60% of all cola drinkers prefer Bolda Cola to Cola Nola.
Scaling: The number of people aged 12-17 that go camping at least twice a year is 1.64 times as many as the number of people aged 18-24 that go camping twice a year.
2. What information do you get from a ratio comparison that you don’t get from a difference comparison?:
In a ratio, you know both numbers in the comparison, and gives you a better proportion and how much one number is out of. In a difference, you only know the amount between the numbers, and you don't know anything about proportion. But if there are more than two numbers in the comparison, things change a bit and get more complicated.
Think about your answers to these questions, discuss your ideas with other students and your teacher, and write a summary of your findings in your journal.:
Ratios, differences, fractions, percents, and scaling are 5 different methods of comparison. They are all more or less accurate and useful comparison methods. It’s good that you can represent comparisons in more than one way, because some comparisons cover more than others. When comparing different things, you’ll need to use all the methods of comparisons because one comparison can give different information than the other. So, a bit like a table, graph, and a written report, all comparison methods are useful at different times.